{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,5,7]],"date-time":"2024-05-07T05:08:59Z","timestamp":1715058539286},"reference-count":10,"publisher":"Oxford University Press (OUP)","issue":"7","license":[{"start":{"date-parts":[[2020,7,20]],"date-time":"2020-07-20T00:00:00Z","timestamp":1595203200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2020,10,23]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>We prove that every locally constant constructive function on an interval is in fact a constant function. This answers a question formulated by Andrej Bauer [ 1]. As a related result, we show that an interval consisting of constructive real numbers is in fact connected but can be decomposed into the disjoint union of two sequentially closed nonempty sets.<\/jats:p>","DOI":"10.1093\/logcom\/exaa038","type":"journal-article","created":{"date-parts":[[2020,6,25]],"date-time":"2020-06-25T19:26:15Z","timestamp":1593113175000},"page":"1425-1428","source":"Crossref","is-referenced-by-count":2,"title":["Locally constant constructive functions and connectedness of intervals"],"prefix":"10.1093","volume":"30","author":[{"given":"Viktor","family":"Chernov","sequence":"first","affiliation":[{"name":"St Petersburg State Economics University, Department of Applied Mathematics and Economico-Mathematical Methods, 21 Sadovaya, St Petersburg 191023, Russia"}]}],"member":"286","published-online":{"date-parts":[[2020,7,20]]},"reference":[{"key":"2020101308243777700_ref1","volume-title":"Private email communication","author":"Bauer","year":"2020"},{"key":"2020101308243777700_ref2","volume-title":"Constructive Analysis Grundlehren der Mathematischen Wissenschaften (Fundamental Principles of Mathematical Sciences), vol. 279. Springer, Berlin","author":"Bishop","year":"1985"},{"key":"2020101308243777700_ref3","first-page":"64","article-title":"Algorithmic operators in constructive complete separable metric spaces Dokl. Akad. Nauk SSSR","volume-title":"English translation in American Mathematical Society Translations","author":"Ceitin","year":"1967"},{"key":"2020101308243777700_ref4","first-page":"98","article-title":"Mean-value theorems in constructive analysis. (in Russian)","volume-title":"English translation in American Mathematical","author":"Ceitin","year":"1971"},{"key":"2020101308243777700_ref5","article-title":"Lectures on constructive mathematical analysis. (in Russian) Monographs in Mathematical Logic and Foundations of Mathematics","volume-title":"Izdat. \u2018Nauka\u2019, Moscow, 1973, pp. 447, English translation in Translations of Mathematical Monographs, 60","author":"Kushner","year":"1984"},{"key":"2020101308243777700_ref6","doi-asserted-by":"crossref","DOI":"10.1090\/trans2\/029\/05","volume-title":"On constructive functions.","author":"Markov","year":"1963"},{"key":"2020101308243777700_ref7","article-title":"On constructive mathematics. (in Russian) Trudy Mat. Inst. Steklov","author":"Markov","year":"1971"},{"key":"2020101308243777700_ref8","article-title":"A constructive map of the square into itself, which moves every constructive point. (in Russian) Dokl. Akad. Nauk SSSR, 152, 55\u201358, 1963","volume":"4","author":"Orevkov","year":"1963","journal-title":"English translation in Soviet Mathematics Doklady"},{"key":"2020101308243777700_ref9","article-title":"Constructive real numbers and constructive functional spaces. (in Russian) Trudy Mat. Inst. Steklov, 67, 15\u2013294, 1962","volume-title":"English translation in Amer","author":"\u0160anin","year":"1968"},{"key":"2020101308243777700_ref10","doi-asserted-by":"crossref","first-page":"145","DOI":"10.2307\/2267043","article-title":"Nicht konstruktiv beweisbare S\u00e4tze der analysis. (German)","volume":"14","author":"Specker","year":"1949","journal-title":"Journal of Symbolic Logic"}],"container-title":["Journal of Logic and Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/academic.oup.com\/logcom\/article-pdf\/30\/7\/1425\/33871915\/exaa038.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"http:\/\/academic.oup.com\/logcom\/article-pdf\/30\/7\/1425\/33871915\/exaa038.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,10,13]],"date-time":"2020-10-13T12:25:01Z","timestamp":1602591901000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/logcom\/article\/30\/7\/1425\/5873891"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,7,20]]},"references-count":10,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2020,7,20]]},"published-print":{"date-parts":[[2020,10,23]]}},"URL":"https:\/\/doi.org\/10.1093\/logcom\/exaa038","relation":{},"ISSN":["0955-792X","1465-363X"],"issn-type":[{"value":"0955-792X","type":"print"},{"value":"1465-363X","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2020,10]]},"published":{"date-parts":[[2020,7,20]]}}}